#!/usr/bin/python

"""Project Euler Solution 041

Copyright (c) 2011 by Robert Vella - robert.r.h.vella@gmail.com

Permission is hereby granted, free of charge, to any person obtaining a copy
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The above copyright notice and this permission notice shall be included in
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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THE SOFTWARE.
"""

import cProfile
from euler.numbers.combinatorics import lexicographic_permutation_at
from euler.numbers.combinatorics import number_of_permutations
from euler.list_functions import first
from euler.numbers.primes import Primes, isprime
from euler.numbers.decimal_base import join_integers

def get_answer():
    """Question:
    
    We shall say that an n-digit number is pandigital if it makes use of all 
    the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital 
    and is also prime.

    What is the largest n-digit pandigital prime that exists?
    """
    
    #Cache for prime numbers.
    primes = Primes()
    
    #The number of digits in the pandigital number. 1 to 9 pandigital numbers 
    #are always divisable by 3 (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45). So 
    #are 1 to 8 pandigital number (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36). 
    #Therefore none of the numbers in these ranges are prime. There, the 
    #highest possible 1 to n pandigital prime has to be a 1 to 7 pandigital.
    number_of_digits = 7
    
    #The index of the last pandigital number with length = number_of_digits.
    highest_range = int(
                        number_of_permutations(
                                               number_of_digits,
                                               number_of_digits
                                            )
                    ) - 1
    
    #The digits in the pandigital number.
    digits = xrange(1, number_of_digits + 1)
    
    def get_1_to_7_pandigital(n):
        """Returns the 1 to 7 pandigital at index [n]."""
        return join_integers(lexicographic_permutation_at(digits, n))
    
    
    #All the 1 to 7 pandigitals in reverse order.
    pandigitals_1_to_7 = (get_1_to_7_pandigital(n) 
                                    for n in xrange(highest_range, -1, -1))
    
    #Return result.
    return first(
                pandigital_1_to_7 
                    for pandigital_1_to_7 in pandigitals_1_to_7
                    if isprime(pandigital_1_to_7, primes)
               )
    
    
if __name__ == "__main__":
    cProfile.run("print(get_answer())")
